Dynamic tuning in wireless energy transfer systems

ABSTRACT

Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for dynamically tuning circuit elements. One aspect includes a variable capacitance device. The device includes a first capacitor, a first switch, a second capacitor, a second switch, and control circuitry. The control circuitry is configured to adjust respective capacitances of the first and second capacitors by causing a first control signal to be applied to the first-switch control terminal for a duration of time in response to detecting a zero voltage condition across the first switch, and by causing a second control signal to be applied to the second-switch control terminal for the duration of time in response to detecting a zero voltage condition across the second switch.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to U.S. Provisional Patent Application No. 62/244,799, filed on Oct. 22, 2015, the entire contents of which are incorporated herein by reference.

BACKGROUND

Electronic devices may require the use of tunable circuit components. In some applications, an electronic device may need to adjust the values of one or more circuit components to match impedances between different portions of a circuit, such as in a dynamic impedance matching network. Existing tunable circuit components may have a limited dynamic range of values, imprecise tuning capabilities, or high power losses. In some cases, existing tunable circuit components may be unusable in high power circuits such as a wireless power transfer system having large voltage swings.

SUMMARY

In general, the disclosure features dynamically tunable circuit elements and related tuning circuits. In a first aspect, the disclosure features a variable capacitance device including a first capacitor, a first switch, a second capacitor, a second switch, and control circuitry. The first capacitor includes a first-capacitor first terminal and a first-capacitor second terminal, where the first-capacitor first terminal is electrically connected to a ground. The first switch includes a first-switch first terminal, a first-switch second terminal, and a first-switch control terminal. The first-switch first terminal is electrically connected to the first-capacitor first terminal, and the first-switch second terminal is electrically connected to the first-capacitor second terminal. The second capacitor includes a second-capacitor first terminal and a second-capacitor second terminal, where the second-capacitor first terminal is electrically connected to the ground. The second switch includes a second-switch first terminal, a second-switch second terminal, and a second-switch a control terminal. The second-switch first terminal is electrically connected to the second-capacitor first terminal, and the second-switch second terminal is electrically connected to the second-capacitor second terminal. The control circuitry is coupled with the first-switch control terminal and the second-switch control terminal. The control circuitry is configured to adjust respective capacitances of the first and second capacitors by causing a first control signal to be applied to the first-switch control terminal for a duration of time in response to detecting a zero voltage condition across the first switch, and by causing a second control signal to be applied to the second-switch control terminal for the duration of time in response to detecting a zero voltage condition across the second switch. The first and second control signals cause the respective first and second switch to close.

This and other implementations can each optionally include one or more of the following features.

A capacitance of the variable capacitance device can depend upon the duration of time for which the first and second control signals are applied to the respective first-switch control terminal and second-switch control terminal. The first switch can be a first transistor and the second switch can be a second transistor. The control circuitry can be configured to receive an input signal and, in response to receiving the input signal, change the duration of time for which the first and second control signals are applied to the respective first-switch control terminal and second-switch control terminal.

In some implementations, the variable capacitance device can include a first comparator and a second comparator. The first comparator can include a first-comparator first input terminal electrically connected to the first-capacitor second terminal. The second comparator can include a second-comparator first input terminal electrically connected to the second-capacitor second terminal. The control circuitry can be coupled with a first-comparator output terminal of the first comparator and a second-comparator output terminal of the second comparator, where the control circuitry configured to detect the zero voltage condition across the first switch based on an output signal of the first comparator, and, in response, cause the first control signal to be applied to the first-switch control terminal for the duration of time; and to detect the zero voltage condition across the second switch based on an output signal of the second comparator, and, in response, cause the second control signal to be applied to the second-switch control terminal for the duration of time.

In some implementations, the variable capacitance device can include a third comparator and a fourth comparator. The third comparator can include a third-comparator first input terminal electrically connected to a first reference voltage and a third-comparator second input terminal electrically connected to the first-switch control terminal. The fourth comparator can include a fourth-comparator first input terminal electrically connected to a second reference voltage and a fourth-comparator second input terminal electrically connected to the second-switch control terminal. The control circuitry can be coupled with a third-comparator output terminal of the third comparator and a fourth-comparator output terminal of the fourth comparator. The control circuitry can be configured to: detect a first ON condition at the first-switch control terminal based on an output signal of the third comparator. Determine a first time difference, where the first time difference being a difference in time from detecting the zero voltage condition across the first switch and detecting the first ON condition at the first-switch control terminal. Adjust a first timing of when the first control signal is applied to the first-switch control terminal so as to reduce the first time difference. Detect a second ON condition at the second-switch control terminal based on an output signal of the fourth comparator. Determine a second time difference, where the second time difference being a difference in time from detecting the zero voltage condition across the second switch and detecting the second ON condition at the second-switch control terminal. And, adjust a second timing of when the second control signal is applied to the second-switch control terminal so as to reduce the second time difference.

In some implementations, the control circuitry can include a pulse width modulation (PWM) generator. The PWM generator can include a first output terminal electrically connected to the first-switch control terminal and a second output terminal electrically connected to the second-switch control terminal, where the first control signal is a first pulse width modulated signal and the second control signal is a second pulse width modulated signal, and the control circuitry is configured to control characteristics of the first and second pulse width modulated signals.

Adjusting the timing of when the first and second control signals are applied to the respective first-switch control terminal and the second-switch control terminal can include adjusting phases of the first and second pulse width modulated signals. The control circuitry can be configured to receive an input signal and, in response to receiving the input signal, change the duration of time for which the first and second control signals are applied to the respective control terminals of the first switch and the second switch by adjusting respective duty cycles of the first and second pulse width modulated signals.

In some implementations, the variable capacitance device can include a third comparator and a fourth comparator. The third comparator can include a third-comparator first input terminal electrically connected to a first reference voltage and a third-comparator second input terminal electrically connected to the first-switch control terminal. The fourth comparator can include a fourth-comparator first input terminal electrically connected to a second reference voltage and a fourth-comparator second input terminal electrically connected to the second-switch control terminal. And, the control circuitry can include a controller, a first counter, and a second counter. The first counter can be coupled with the first-comparator output terminal, the third-comparator output terminal, and the controller. In addition, the first counter can be configured to start a first timer in response to receiving a zero voltage signal from the first comparator, stop the first timer in response to receiving a first ON condition signal from the third comparator, and send a signal indicating an elapsed time of the first timer to the controller. The second counter can be coupled with the second-comparator output terminal, the fourth-comparator output terminal, and the controller. In addition, the second counter can be configured to start a second timer in response to receiving a zero voltage signal from the second comparator, stop the second timer in response to receiving a second ON condition signal from the fourth comparator, and send a signal indicating an elapsed time of the second timer to the controller. And, the controller can be configured to adjust a first timing of when the first control signal is applied to the first-switch control terminal, based on the first-time-difference signal, so as to reduce the first time difference, and adjust a second timing of when the second control signal is applied to the second-switch control terminal, based on the second-time-difference signal, so as to reduce the second time difference.

In some implementations, the control circuitry can include a PWM generator coupled with the controller. The PWM generator can include a first output terminal electrically connected to the first-switch control terminal and a second output terminal electrically connected to the second-switch control terminal, where the first control signal is a first pulse width modulated signal and the second control signal is a second pulse width modulated signal. The controller can be configured to control characteristics of the first and second pulse width modulated signals.

The controller can be one of: a microcontroller, a computer processor, a field programmable logic array (FPGA), or an application specific integrated circuit (ASIC).

In some implementations, detecting the zero voltage condition across the first switch based on an output signal of the first comparator, and, in response, causing the first control signal to be applied to the first-switch control terminal can include: determining a first phase difference between a first-comparator output signal and a third-comparator output signal, generating a third reference voltage based the first phase difference, and causing the first control signal to be applied to the first-switch control terminal upon detecting that a voltage signal at the first-switch second terminal has crossed a voltage value equal to the third reference voltage. Detecting the zero voltage condition across the second switch based on an output signal of the second comparator, and, in response, cause the second control signal to be applied to the second-switch control terminal can include: determining a second phase difference between a second-comparator output signal and a fourth-comparator output signal, generating a fourth reference voltage based the second phase difference, and causing the second control signal to be applied to the second-switch control terminal upon detecting that a voltage signal at the second-switch second terminal has crossed a voltage value equal to the fourth reference voltage.

In some implementations, the control circuitry includes a first phase detection circuit, a first integrator circuit, a fifth comparator, a first flip-flop, a second phase detection circuit, a second integrator circuit, a sixth comparator, a second flip-flop, and a controller. The first phase detection circuit is coupled with the first-comparator output terminal and a third-comparator output terminal of the third comparator. The first integrator circuit is coupled with the first phase detection circuit. The fifth comparator includes a fifth-comparator output terminal, a fifth-comparator first input terminal electrically connected to the first-capacitor second terminal, and a fifth-comparator second input terminal coupled with the first integrator circuit. The first flip-flop includes a first-flip-flop reset terminal, a first-flip-flop clock terminal electrically connected to the fifth-comparator output terminal, and a first-flip-flop output terminal electrically connected to the first-switch control terminal. The second phase detection circuit is coupled with the second-comparator output terminal and a fourth-comparator output terminal of the fourth comparator. The second integrator circuit is coupled with the second phase detection circuit. The sixth comparator includes a sixth-comparator output terminal, a sixth-comparator first input terminal electrically connected to the second-capacitor second terminal, and a sixth-comparator second input terminal coupled with the second integrator circuit. The second flip-flop includes a second-flip-flop reset terminal, a second-flip-flop clock terminal electrically connected to the sixth-comparator output terminal, and a second-flip-flop output terminal electrically connected to the second-switch control terminal. The controller is coupled with the first flip-flop and the second flip-flop and is configured to provide a first reset signal to the first flip-flop after the duration of time and to provide a second reset signal to the second flip-flop after the duration of time. The controller can be a PWM generator, where the first reset signal is a first pulse width modulated signal, and the second reset signal is a second pulse width modulated signal.

In a second aspect, the disclosure features a wireless energy transfer system includes a split coil resonator and a variable capacitance device. The split coil resonator includes a first winding magnetically coupled with a second winding. The variable capacitance device includes a first capacitor, a first switch, a second capacitor, a second switch, and control circuitry. The first capacitor includes a first-capacitor first terminal and a first-capacitor second terminal, the first-capacitor first terminal electrically connected to a ground, and the first-capacitor second terminal electrically connected to a first-winding terminal of the first winding of the split coil resonator. The first switch includes a first-switch first terminal, a first-switch second terminal, and a first-switch control terminal, the first-switch first terminal electrically connected to the first-capacitor first terminal, and the first-switch second terminal electrically connected to the first-capacitor second terminal. The second capacitor includes a second-capacitor first terminal and a second-capacitor second terminal, the second-capacitor first terminal electrically connected to the ground, and the second-capacitor second terminal electrically connected to a second-winding terminal of the second winding of the split coil resonator. The second switch comprising a second-switch first terminal, a second-switch second terminal, and a second-switch a control terminal, the second-switch first terminal electrically connected to the second-capacitor first terminal, and the second-switch second terminal electrically connected to the second-capacitor second terminal. The control circuitry is coupled with the first-switch control terminal and with the second-switch control terminal. The control circuitry is configured to adjust respective capacitances of the first and second capacitors by causing a first control signal to be applied to the first-switch control terminal for a duration of time in response to detecting a zero voltage condition across the first switch, and by causing a second control signal to be applied to the second-switch control terminal for the duration of time in response to detecting a zero voltage condition across the second switch. The first and second control signals cause the respective first and second switch to close.

This and other implementations can each optionally include one or more of the following features. In addition, the variable capacitance device can include any of the features described above.

In some implementations, the wireless energy transfer system can include a third capacitor and a fourth capacitor. The third capacitor can include a third-capacitor first terminal and a third-capacitor second terminal, the third-capacitor first terminal electrically connected to the first-winding terminal, and the third-capacitor second terminal electrically connected to the first-capacitor second terminal. And, the fourth capacitor can include a fourth-capacitor first terminal and a fourth-capacitor second terminal, the fourth-capacitor first terminal electrically connected to the second-winding terminal, and the fourth-capacitor second terminal electrically connected to the second-capacitor second terminal. The wireless energy transfer system can include a fixed impedance matching network coupled with a first-winding second terminal of the first winding and a second-winding second terminal of the second winding.

In some implementations, the wireless energy transfer system can include a third capacitor comprising a third-capacitor first terminal and a third-capacitor second terminal, the third-capacitor first terminal electrically connected to the first-winding terminal, and the third-capacitor second terminal electrically connected to the second-winding terminal.

In a third aspect, the disclosure features a zero voltage switching device including a switch, a first comparator, a second comparator and a controller. The switch includes a first terminal, a second terminal, and a control terminal. The first comparator includes a first input terminal electrically connected to the second terminal of the switch and a second input terminal electrically connected to the first terminal of the switch. The second comparator includes a first input terminal electrically connected to a reference voltage and a second input terminal electrically connected to the control terminal of the switch. The controller is coupled to respective output terminals of the first and second comparators. And, the controller is configured to: detect a zero voltage condition across the switch based on an output of the first comparator, and, in response, cause a control signal to be applied to the control terminal of the switch, wherein the control signal causes the switch to close. Detect an ON condition at the control terminal of the first switch based on an output of the second comparator. Determine a time difference, the time difference being a difference in time from detecting the zero voltage condition across the switch and detecting the ON condition at the control terminal of the switch. And, adjusting a timing of when the control signal is applied to the control terminal of the switch so as to reduce the time difference.

This and other implementations can each optionally include one or more of the following features.

The reference voltage can be selected based on characteristics of the switch. The switch can be a field effect transistor, where the control terminal is a gate of the transistor, the first terminal is one of a source or a drain of the transistor, and the second terminal is the other of the source or the drain of the transistor. The reference voltage can be selected based on the threshold voltage of the transistor. The controller can be one of: a microcontroller, a computer processor, a field programmable logic array (FPGA), or an application specific integrated circuit (ASIC).

In some implementations, the zero voltage switching device includes a PWM generator coupled with the controller, where the PWM generator includes an output terminal electrically connected to the control terminal of the switch. The control signal can be a pulse width modulated signal, and the controller can be configured to control characteristics of the pulse width modulated signal. Adjusting the timing of when the control signal is applied to the control terminal of the switch can include adjusting a phase of the pulse width modulated signal.

In a fourth aspect, the disclosure features a zero voltage switching device including a switch, a first comparator, a second comparator, and control circuitry. The switch includes a first terminal, a second terminal, and a control terminal. The first comparator includes a first-comparator output terminal and a first-comparator first input terminal electrically connected to the first terminal of the switch. The second comparator includes a second-comparator output terminal, a second-comparator first input terminal electrically connected to a first reference voltage, and a second-comparator second input terminal electrically connected to the control terminal of the switch. The control circuitry is coupled with the first-comparator output terminal and the second-comparator output terminal. In addition, the control circuitry is configured to: determine a phase difference between a first-comparator output signal and a second-comparator output signal, generate a second reference voltage based the phase difference, and cause a control signal to be applied to the switch control terminal upon detecting that a voltage signal at one of the first terminal or second terminal of the switch has crossed a voltage value equal to the second reference voltage.

In some implementations, the control circuitry includes, a phase detection circuit, an integrator circuit, a third comparator, a flip-flop, and a controller. The phase detection circuit can be coupled with the first-comparator output terminal and the second-comparator output terminal. The integrator circuit can be coupled with the phase detection circuit. The third comparator can include a third-comparator output terminal, a third-comparator first input terminal electrically connected to the first terminal of the switch, and a third-comparator second input terminal coupled with the integrator circuit. The flip-flop can include a reset terminal, a clock terminal electrically connected to the third-comparator output terminal, and an output terminal electrically connected to the control terminal of the switch. And, the controller can be coupled with the reset terminal of the flip-flop, and configured to provide a reset signal to the flip-flop.

The controller can be configured to provide the reset signal to turn the switch OFF after a switch ON duration. The switch can be a field effect transistor, where the control terminal is a gate of the transistor, the first terminal is one of a source or a drain of the transistor, and the second terminal is the other of the source or the drain of the transistor.

The first reference voltage can be selected based on the threshold voltage of the transistor. The phase detection circuit can be to determine a phase difference between an output signal from the first comparator and an output signal from the second comparator. The controller can be a PWM generator and the reset signal is a PWM signal.

Particular implementations of the subject matter described in this specification can be implemented so as to realize one or more of the following advantages. Implementations may permit the use of lower operating voltages for tuning circuit components. Some implementations may reduce voltage and current stresses on tunable circuit components. Some implementations may permit dynamic balancing of resonator coils. Some implementations may improve the accuracy of zero voltage switching (ZVS) controls.

Embodiments of the devices, circuits, and systems disclosed can also include any of the other features disclosed herein, including features disclosed in combination with different embodiments, and in any combination as appropriate.

The details of one or more implementations of the subject matter described in this specification are set forth in the accompanying drawings and the description below. Other features, aspects, and advantages of the subject matter will be apparent from the description, the drawings, and the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a block diagram of an example of a wireless power transfer system.

FIG. 2 shows a block diagram of an example wireless power transfer system including an impedance matching network.

FIG. 3 depicts an example of a dynamically tunable capacitor circuit in accordance with implementations of the present disclosure.

FIGS. 4A-4C depict examples of voltage signals applied to the tunable capacitor circuit.

FIG. 5 depicts an example of a wireless energy transfer system including a dynamically tunable capacitor circuit.

FIG. 6 depicts the dynamically tunable capacitor circuit with an example of a first implementation of the control circuitry.

FIG. 7 depicts the dynamically tunable capacitor circuit with an example of a second implementation of the control circuitry.

FIG. 8 depicts the dynamically tunable capacitor circuit with an example of a third implementation of the control circuitry.

FIGS. 9A-9D depict graphs of exemplary control signals in the control circuitry of the third implementation.

Like reference numbers and designations in the various drawings indicate like elements.

DETAILED DESCRIPTION

Wireless energy transfer systems described herein can be implemented using a wide variety of resonators and resonant objects. As those skilled in the art will recognize, important considerations for resonator-based power transfer include resonator quality factor and resonator coupling. Extensive discussion of such issues, e.g., coupled mode theory (CMT), coupling coefficients and factors, quality factors (also referred to as Q-factors), and impedance matching is provided, for example, in U.S. patent application Ser. No. 13/428,142, published on Jul. 19, 2012 as US 2012/0184338, in U.S. patent application Ser. No. 13/567,893, published on Feb. 7, 2013 as US 2013/0033118, and in U.S. patent application Ser. No. 14/059,094, published on Apr. 24, 2014 as US 2014/0111019. The entire contents of each of these applications are incorporated by reference herein.

Power transfer systems may rely on electronic circuits such as rectifiers, AC (Alternating Current) to DC (Direct Current) converters, impedance matching circuits, and other power electronics to condition, monitor, maintain, and/or modify the characteristics of the voltage and/or current used to provide power to electronic devices. Power electronics can provide power to a load with dynamic input impedance characteristics. In some cases, in order to enable efficient power transfer, a dynamic impedance matching network is provided to match varying load impedances to that of the power source.

In some applications such as wireless power transfer, load impedances for a wireless power supply device may vary dynamically. In such applications, impedance matching between a load, such as a resonator coil, and a power supply of the device may be required to prevent unnecessary energy losses and excess heat. For example, the impedance associated with a resonator coil may be dynamic, in which case, a dynamic impedance matching network can be provided to match the varying power supply impedance (e.g., a device resonator) to that of the device. In the case of a wirelessly powered device, power supply impedances (e.g., a device resonator coil) may be highly variable. Therefore, an impedance matching network can be supplied between the device resonator coil and the power source of the device (e.g., battery or battery charging circuitry) to promote efficient transfer of power. Accordingly, power transfer systems transferring and/or receiving power via highly resonant wireless energy transfer, for example, may be required to configure or modify impedance matching networks to maintain efficient power transfer. The power electronics used in existing devices may not be capable of accurately detecting or measuring impedance mismatches or of rapidly accounting for impedance variations.

While the impedance matching circuits, methods, and systems disclosed herein are discussed in the context of a wireless power transfer system, it should be appreciated that they may be useful with other electronic devices as well. In some cases, the disclosed control circuitry and ZVS techniques may be used in other applications such as, for example, high power amplifiers and power supplies.

FIG. 1 shows a block diagram of an example of a wireless power transfer system 100. The system 100 includes a wireless power source 102 and a wirelessly powered or wirelessly charged device 104. Wirelessly powered or wirelessly charged devices 104 can include, for example, electronic devices such as laptops, smartphones, tablets, and other mobile electronic devices that are commonly placed on desktops, tabletops, bar tops, and other types of surfaces. The device 104 includes a device resonator 108D, device power and control circuitry 110, and a wirelessly powered or wirelessly charged electronic device 112, to which either DC or AC or both AC and DC power is transferred. The wireless power source 102 includes source power and control circuitry 106 and a source resonator 108S. The electronic device 112 or devices that receive power from the device resonator 108D and device power and control circuitry 110 can be, for example, an electronic device such as a laptop, smartphone, and other mobile electronic devices. The device resonator 108D and device circuitry 110 delivers power to the device/devices 112 that can be used to recharge the battery of the device/devices, power the device/devices directly, or both when in the vicinity of the source resonator 108S.

The power source 102 can be powered from a number of DC or AC voltage, current or power sources including, for example, a USB (Universal Serial Bus) port of a computer. In addition, the source 102 can be powered from the electric grid, from a wall plug, from a battery, from a power supply, from an engine, from a solar cell, from a generator, or from another source resonator. The source power and control circuitry 106 can include circuits and components to isolate the source electronics from the power supply, so that any reflected power or signals are not coupled out through the source input terminals.

The source power and control circuitry 106 can drive the source resonator 108S with alternating current, such as with a frequency greater than 10 kHz and less than 100 MHz (e.g., 6.78 MHz). The source power and control circuitry 106 can include, for example, impedance matching circuitry, a DC-to-DC converter, an AC-to-DC converter, or both an AC-to-DC converter and a DC-to-DC converter, an oscillator, and a power amplifier.

The device power and control circuitry 110 can be designed to transform alternating current power from the device resonator 108D to stable direct current power suitable for powering or charging one or more devices 112. The device power and control circuitry 110 can be designed to transform an alternating current power at one frequency (e.g., 6.78 MHz) from the device resonator to alternating current power at a different frequency suitable for powering or charging one or more devices 112. The power and control circuitry can include, for example, impedance matching circuitry, rectification circuitry, voltage limiting circuitry, current limiting circuitry, AC-to-DC converter circuitry, DC-to-DC converter circuitry, DC-to-AC converter circuitry, AC-to-AC converter circuitry, and battery charge control circuitry.

The power source 102 and the device 104 can have tuning capabilities, for example, dynamic impedance matching circuits, that allow adjustment of operating points to compensate for changing environmental conditions, perturbations, and loading conditions that can affect the operation of the source and device resonators and the efficiency of the energy transfer. The tuning capability can also be used to multiplex power delivery to multiple devices, from multiple sources, to multiple systems, to multiple repeaters or relays, and the like. The tuning capability can be controlled automatically, and may be performed continuously, periodically, intermittently or at scheduled times or intervals. In some implementations, manual input can be used to configure a control algorithm for tuning the impedance matching circuits.

The power source 102 and the device 104 resonators may be separated by many meters or they may be very close to each other or they may be separated by any distance in between. The source and device resonators 108S, 108D may be offset from each other laterally or axially. The source and device resonators 108S, 108D may be directly aligned (no lateral offset). The source and device resonators 108S, 108D may be oriented so that the surface areas enclosed by their inductive elements are approximately parallel to each other. The source and device resonators 108S, 108D may be oriented so that the surface areas enclosed by their inductive elements are approximately perpendicular to each other, or they may be oriented for any relative angle (0 to 360 degrees) between them. Such variations in the physical arrangement between the source and device resonators 108S, 108D may affect power coupling between the resonators 108S, 108D, and thereby, alter impedances exhibited by the resonators 108S, 108D to the source power and control circuitry 106 or device power and control circuitry 110, respectively.

FIG. 2 shows a block diagram of an example wireless power transfer system 200 including an impedance matching network (IMN) 204 and IMN control circuitry 208. The system 200 can, for example, be implemented as part of either the wireless power source 102 or the wirelessly powered or charged device 104 of FIG. 1. The system 200 includes a power supply 202, an IMN 204, a load 206, and IMN control circuitry 208. The load 206 can be, for example, the source resonator 108S of the wireless power source 102. In another example, the power supply 202 can be the source power and control circuitry 106 of the wireless power source 102. The power supply 202 can be the device resonator 108D of the device 104. The load 206 can be the electronic device 112 powered by or a battery of the electronic device 112 charged by the device resonator 108D. The impedance exhibited by either the load 206 or the power supply 202 may be dynamic and vary based on, for example, a physical position of a device 104 (e.g., a device resonator 108D) in relation to a wireless power source 102 (e.g., a source resonator 108S).

The impedance-matching network 204 can be designed to maximize the power delivered between power supply 202 and the load 206 at a desired frequency (e.g., 6.78 MHz). The impedance matching components in the IMN 204 can be chosen and connected so as to preserve a high-Q value of the resonator. Depending on the operating conditions, the components in the IMN 204 can be automatically tuned to control the power delivered from the power supply 202 to the load 206, for example, to maximize efficient transfer of power from a power supply 202 to a source resonator (e.g., load 206 of a wireless power source 102).

The IMN 204 components can include, for example, a capacitor or networks of capacitors, an inductor or networks of inductors, or various combinations of capacitors, inductors, diodes, switches, and resistors. The components of the impedance matching network can be adjustable and variable and can be controlled to affect the efficiency and operating point of the system. The impedance matching can be performed by controlling the connection point of the resonator, adjusting the permeability of a magnetic material, controlling a bias field, adjusting the frequency of excitation, and the like. The impedance matching can use or include any number or combination of varactors, varactor arrays, switched elements, capacitor banks, switched and tunable elements, reverse bias diodes, air gap capacitors, compression capacitors, barium zirconium titanate (BZT) electrically tuned capacitors, microelectromechanical systems (MEMS)-tunable capacitors, voltage variable dielectrics, transformer coupled tuning circuits, and the like. The variable components can be mechanically tuned, thermally tuned, electrically tuned, piezo-electrically tuned, and the like. Elements of the impedance matching can be silicon devices, gallium nitride devices, silicon carbide devices, and the like. The elements can be chosen to withstand high currents, high voltages, high powers, or any combination of current, voltage and power. The elements can be chosen to be high-Q elements.

The IMN control circuitry 208 monitors impedance differences between the source 202 and the load 206 and provides control signals to the IMN 204 to tune the IMN 204 or components thereof. In some instances, the IMN control circuitry 208 can include ZVS circuitry to reduce power losses and increase the overall efficiency of the circuit. For example, ZVS circuitry can control switching operations within the IMN 204 to occur when a voltage (e.g., a voltage across one or more components) is near or at zero. In so doing, the IMN control circuitry 208 may minimize transients and power losses.

In some implementations, the IMN 204 can include a fixed IMN and a dynamic IMN. For example, a fixed IMN may provide impedance matching between portions of the system with static impedances or to grossly tune a circuit to a known dynamic impedance range. In some implementations, a dynamic IMN can be further composed of a coarsely adjustable IMN and a finely adjustable IMN. For example, the coarsely adjustable IMN can permit coarse impedance adjustments within a dynamic impedance range and the finely adjustable IMN can be used to fine tune the overall impedance of the IMN 204. In another example, the coarsely adjustable IMN can attain impedance matching within a desirable impedance range and the finely adjustable IMN can achieve a more precise impedance around a target within the desirable impedance range.

FIG. 3 depicts an example of a dynamically tunable capacitor circuit 300. The tunable capacitor circuit 300 includes two capacitors 302 a, 302 b of equal capacitance (C) electrically connected in series with a ground connection 310 between them. Each capacitor 302 a, 302 b has an associated shorting switch 304 a, 304 b electrically connected in parallel with the respective capacitor 302 a, 302 b. The shorting switches 304 a, 304 b can be transistors such as, for example, metal-oxide-semiconductor field-effect transistors (MOSFET), junction gate field-effect transistors (JFET), or bipolar junction (BJT) transistors. Both the capacitors 302 a, 302 b and switches 304 a, 304 b can be ground referenced, for example, for use in high voltage circuits such as circuits including wireless power transmission coils. For example, connecting one terminal each of the capacitors 302 a, 302 b and each switch 304 a, 304 b to ground may permit the use of lower switch control voltages (e.g., less than 5 V) and eliminate a need for level shifting or other special control or isolation circuitry.

The effective capacitance of the combined capacitors 302 a, 302 b can be controlled by varying the period of time that the capacitors 302 a, 302 b are shorted during portions of a cycle of an AC input signal (I_(AC)) applied to the capacitors 302 a, 302 b. In other words, effective capacitance can be controlled by varying the period of time that the switches 304 a, 304 b are closed (or “ON” in the case of transistor switches (T_(ON))). Together, the capacitors 302 a, 302 b and switches 304 a, 304 b are controlled so as to function as a single capacitor with an effective capacitance

${{\left( C_{eff} \right)\mspace{14mu}{equal}\mspace{14mu}{to}\mspace{14mu} C_{eff}} = {\frac{C}{2}\left( {1/\left( {1 - {T_{ON}*f}} \right)} \right)}},$ where f is the frequency (e.g., 6.78 MHz) of the AC signal (I_(AC)) applied to the capacitors 302 a, 302 b. The tunable capacitor circuit 300, thus, has a range of effective capacitance (C_(eff)) from 0 to C/2. The tuning resolution, or precision, of the tunable capacitor circuit 300 is determined by the number of possible values for T_(ON) in some implementations. Thus, the tuning resolution of the tunable capacitor circuit 300 need be limited only by the timing resolution of T_(ON).

FIGS. 4A-4C depict examples of AC voltage signals applied to the tunable capacitor circuit 300. Referring to FIGS. 3, 4A, and 4B, FIGS. 4A and 4B depict graphs 400 and 420 of voltage signals at Va and Vb in the tunable capacitor circuit 300. The voltage signal at Va represents the voltage across capacitor 302 a, and the voltage signal at Vb represents the voltage across capacitor 302 b. The voltage signals are shown with a frequency of 6.78 MHz.

In FIG. 4A, for example, the switches 304 a, 304 b are closed (i.e., capacitors 302 a, 302 b are shorted) for 15 ns during each cycle of the voltage signals Va and Vb. In other words, T_(ON) is equal to 15 ns in FIG. 4A resulting in a peak amplitude of approximately 50V. In FIG. 4B, for example, the switches 304 a, 304 b are closed (i.e., capacitors 302 a, 302 b are shorted) for 60 ns during each cycle of the voltage signals Va and Vb. In other words, T_(ON) is equal to 60 ns in FIG. 4B resulting in a peak amplitude of approximately 33V. As seen by the difference in amplitude between signals Va and Vb in FIG. 4A compared to signals Va and Vb in FIG. 4B a longer T_(ON) time, as shown in FIG. 4B, results in a lower effective capacitance (or effective impedance) of the tunable capacitor circuit 300 as indicated by the lower voltage drop across the respective capacitors 302 a, 302 b. A graph 440 of the overall voltage across the tunable capacitor circuit 300 is shown in FIG. 4C. The voltage signal in FIG. 4C represents Va-Vb, the voltage across both capacitors 302 a, 302 b, with a 60 ns T_(ON) value.

In addition, the switches 304 a, 304 b can be timed to close (turn ON) when the voltage across the associated capacitor 302 a, 302 b (Va or Vb) crosses zero. This timing is illustrated by the zero crossings 402 and 404 of FIGS. 4A and 4B respectively and is referred to as zero voltage switching (ZVS). Precisely time switching of the switches 304 a, 304 b may ensure that the voltage across the tunable capacitor circuit 300 is continuous, and also prevent both large current transients and needless power losses.

Referring again to FIG. 3, the switches 304 a, 304 b, are controlled by control circuitry 306 coupled with respective control terminals (e.g., transistor gate terminals) of switches 304 a, 304 b. The control circuitry 306 controls the effective capacitance of the capacitors by controlling T_(ON) of the switches 304 a, 304 b in accordance with a tuning input. In addition, the control circuitry 306 controls the ZVS timing of the switches 304 a, 304 b by monitoring the voltage or current of a signal applied to the capacitors 302 a, 302 b. The control circuitry 306 can include, for example, a microcontroller, a computer processor, a field programmable logic array (FPGA), or an application specific integrated circuit (ASIC). The control circuitry 306 can include or be coupled to a computer readable storage device such as, for example, random access memory, flash memory, or other appropriate memory device.

Comparators 308 a, 308 b can be used to detect when the voltage across the respective capacitor 302 a, 302 b crosses zero. For example, the input terminals of comparator 308 a are electrically connected across capacitor 302 a, and the input terminals of comparator 308 b are electrically connected across capacitor 302 b. The respective output terminals of the comparators 308 a, 308 b are coupled with the control circuitry 306.

The control circuitry 306 can detect the zero crossings based on the output signals of comparators 308 a, 308 b and, upon detecting a zero crossing, close the switches 304 a, 304 b for a duration of T_(ON). For example, the control circuitry 306 can detect the zero crossing of the voltage across the capacitor 302 a based on the rising or falling edge of the comparator's 308 a output signal. In response, the control circuitry 306 can apply a control signals to the control terminal switch 304 a to close the switch (e.g., turn the transistor ON) and begin shorting the capacitor 302 a. After the duration T_(ON) expires, the control circuitry 306 re-opens the switch 304 a (e.g., turns the transistor OFF).

The T_(ON) duration can be controlled by, for example, a counter that is part of the control circuitry 306. The duration of the counter (T_(ON)) can be set based on a tuning input signal to the control circuitry 306. For example, an IMN control circuitry 208 (shown in FIG. 2) can transmit one or more tuning control signals to the control circuitry 306. The control circuitry 306 can vary a duration of the counter (T_(ON)) based on the received tuning control signal(s).

The comparators 308 a, 308 b can produce a two-level output signal that alternates when the voltage across the respective capacitor 302 a, 302 b crosses zero. Moreover, the value of the comparator output signal can indicate the polarity of the voltage signals. For example, as shown in FIG. 3, the non-inverting (“+”) input terminal of each comparator 308 a, 308 b is electrically connected to the grounded terminal of its respective capacitor 302 a, 302 b. The inverting (“−”) input terminal of each comparator 308 a, 308 b is electrically connected to the other (non-grounded) terminal of its respective capacitor 302 a, 302 b. In this configuration, each comparator 308 a, 308 b will output a high signal value when the voltage across its respective capacitor 302 a, 302 b is negative and a low signal when the voltage across its respective capacitor 302 a, 302 b is positive.

In some implementations, the comparators 308 a, 308 b can be connected with the input terminals swapped. That is, the inverting (“−”) input terminal of each comparator 308 a, 308 b can be electrically connected to the grounded terminal of its respective capacitor 302 a, 302 b. The non-inverting (“+”) input terminal of each comparator 308 a, 308 b can be electrically connected to the other (non-grounded) terminal of its respective capacitor 302 a, 302 b. In such a configuration, each comparator 308 a, 308 b will output a high signal value when the voltage across its respective capacitor 302 a, 302 b is positive and a low signal when the voltage across its respective capacitor 302 a, 302 b is negative.

In some implementations, the effective capacitances of capacitor 302 a and capacitor 302 b can be tuned independently by, for example, shorting each capacitor 302 a, 302 b for a different duration. For example, the T_(ON) associated with each capacitor 302 a, 302 b may be different, thereby, producing a different effective capacitance for each capacitor. Hence, the effective capacitance of capacitor 302 a can be represented by C_(eff) _(_) _(a)=C_(a)/(1−T_(ON) _(_) _(a)*f), the effective capacitance of capacitor 302 b can be represented by C_(eff) _(_) _(b)=C_(b)/(1−T_(ON) _(_) _(b)*f), and the overall effective capacitance can be represented by the series combination of C_(eff) _(_) _(a) and C_(eff) _(_) _(b).

In some implementations, the comparators 308 a, 308 b can be replaced by phase detection devices. For example, a voltage or current sensor (e.g., a Rogowski coils) can be used to monitor the voltage across or current through a circuit component (e.g., capacitors 302 a, 302 b). A phase detection device or circuitry can detect and track the phase of the voltage or current and the control circuitry 306 (e.g., a microcontroller or processor) can time the ZVS of the switches 304 a, 304 b based on the phase of the monitored voltage or current. For example, the control circuitry 306 can determine the zero crossings of the monitored voltage or current based on the detected phase, and control the switches 304 a, 304 b accordingly.

In some examples, the tunable capacitor circuit 300 can be implemented without a ground reference between the capacitors 302 a, 302 b. For example, the tunable capacitor circuit 300 can be isolated from high voltages using isolation circuitry, such as opto-couplers, isolation transformers, and the like, for example.

FIG. 5 depicts an example of a wireless energy transfer system 500 including a dynamically tunable capacitor circuit 300. The wireless energy transfer system 500 includes the tunable capacitor circuit 300 of FIG. 3, a split-coil 502, an optional fixed IMN 508, and power source or device 510 that either provides power to the split-coil 502 (e.g., power source 102) or receives power from the split-coil 502 (e.g., a wirelessly powered/charged electronic device 112).

The tunable capacitor circuit 300 is coupled with the split-coil 502 and can be tuned to adapt the impedance of the wireless energy transfer system 500 to a varying impedance of the split-coil 502. As described in reference to FIG. 1 above, the split-coil 502 can be used to wirelessly transfer energy to or receive energy from another resonator coil (e.g., a corresponding device or source resonator coil, respectively). The effective impedance of the split-coil 502 may vary dynamically based on, for example, environmental factors (e.g., interfering objects), orientation between resonator coils, distance between resonator coils, etc. The tunable capacitor circuit 300 can be adjusted to compensate for such variations in the effective impedance of the split-coil 502.

The split-coil 502 includes two windings 504 and 506 that are coupled so as to function as one resonator coil. In embodiments, the two windings 504 and 506 are magnetically coupled. In some implementations, the split-coil 502 can be two separate coils coupled by a capacitor. Each winding 504, 506 has two input terminals 507. The tunable capacitor circuit 300 is connected in series between the windings 504, 506 to one input terminal 507 of each winding 504, 506. The split-coil design allows for a ground-reference point to be established between the windings 504, 506 of the split-coil 502. As a result, impedance matching circuitry such as the tunable capacitor circuit 300 and capacitors C₁, C₂, and C₃ can be connected to the resonator 502 and operated at lower voltages without the need of isolation circuits such as galvanic isolation circuits.

The wireless energy transfer system 500 also can include capacitors C₁, C₂, and/or C₃. These capacitors can be either fixed or variable capacitors. Each of capacitors C₁, C₂, and C₃ can represent, for example, a number or combination of varactors, varactor arrays, capacitor banks, air gap capacitors, compression capacitors, barium zirconium titanate (BZT) electrically tunable capacitors, or microelectromechanical systems (MEMS)-tunable capacitors. For example, capacitors C₁, C₂, and/or C₃ can represent a coarsely adjustable impedance matching network used in combination with the tunable capacitor circuit 300. For instance, capacitors C₁, C₂, and/or C₃ can be used to grossly tune a circuit to a known dynamic impedance range or can provide coarse impedance adjustments while the tunable capacitor circuit 300 provides fine impedance adjustments. For example, the capacitors C₁, C₂, and/or C₃ can permit coarse impedance adjustments within a dynamic impedance range and the tunable capacitor circuit 300 can be used to perform fine impedance adjustments.

Although circuit elements C₁, C₂, and/or C₃ are represented and described as capacitors, in some implementations, they can be replaced by or used in combination with other impedance matching components. For example, capacitors C₁, C₂, and/or C₃ can be replaced by or used in combination with inductors, diodes, and resistors.

As noted above, in some implementations, the effective capacitances of capacitor 302 a and capacitor 302 b can be tuned independently by, for example, shorting each capacitor 302 a, 302 b for a different duration. For example, when combined with a split-coil 502, independent tuning of capacitors 302 a, 302 b may be used to correct for imbalances in the respective windings 504, 506 of the split-coil 502. For example, a second resonator coil (e.g., a resonator coil to which power is being transferred) may be placed next to the split-coil 502, but misaligned slightly so as to create an impedance imbalance between the windings 504, 506. For example, the impedance of winding 504 may become more inductive than that of winding 506. The wireless energy transfer system 500 can correct for such imbalance by, for example, adjusting T_(ON) _(_) _(a) to increase the effective capacitance of capacitor 302 a, adjusting T_(ON) _(_) _(b) to decrease the effective capacitance of capacitor 302 b, or adjusting T_(ON) _(_) _(a) and T_(ON) _(_) _(b) in combination to re-balance the windings 504, 506.

The fixed IMN 508 can include, for example, a capacitor or networks of capacitors, an inductor or networks of inductors, or various combinations of capacitors, inductors, diodes, and resistors. For example, the fixed IMN 508 may provide impedance matching between portions of the system 500 with static impedances or to grossly tune the system 500 to a known dynamic impedance range (e.g., a dynamic impedance range of the split-coil 502).

FIG. 6 depicts the dynamically tunable capacitor circuit 600 with an example of a first implementation of the control circuitry 606. The control circuitry 606 includes a flip-flop 602 a, 602 b and a T_(ON) counter 604 a, 604 b associated with each capacitor 302 a, 302 b. The flip-flops 602 a, 602 b are illustrated as D flip-flops, however, they may be implemented using other types of flip-flops or gated latch circuits. As illustrated in FIG. 6, the control circuitry 606 is symmetric, so, for simplicity, the control circuitry will be described in the context of one capacitor (capacitor 302 a).

The comparator 308 a and the flip-flop 602 a in combination control the ZVS of the switch 304 a. The comparator 308 a changes the state of its output signal when the voltage across the capacitor 302 a (Va) crosses zero, as described above in reference to FIG. 3. The comparator 308 a output signal is applied to an edge triggered gating (clock) input of the flip-flop 602 a. The input (D) of the flip-flop 602 a is tied to a high (e.g., 5V) input signal VDD (e.g., 5V). The output terminal (Q) of the flip-flop 602 a is electrically connected to the control terminal of the switch 304 a (e.g., transistor gate) and a counter-start terminal of the T_(ON) counter 504 a. When the flip-flop 602 a detects an appropriate edge (rising or falling) in the comparator 308 a output signal, the flip-flop turns switch 304 a ON to short capacitor 302 a and triggers the T_(ON) counter 604 a to begin timing the duration T_(ON).

An output terminal of the T_(ON) counter 604 a is electrically connected to the CLR input terminal of the flip-flop 602 a. Upon expiration of the duration T_(ON), the T_(ON) counter 604 a generates a CLR signal to clear the output of the flip-flop 602 a (e.g., reset to low or “0”), thereby, turning the switch 304 a OFF. In addition, the T_(ON) counter 604 a can receive a tuning input signal to set the duration of T_(ON) and control the effective capacitance of the capacitor 302 a. Furthermore, the resolution of the effective capacitance for capacitor 302 a is determined by the count increment of the T_(ON) counter 604 a. For example, a T_(ON) counter 604 a having a smaller count increment will allow for more precise control of the effective capacitance of the capacitor 302 a.

FIG. 7 depicts the dynamically tunable capacitor circuit 700 with an example of a second implementation of the control circuitry 706. The control circuitry 706 includes a controller 702, counters 704 a, 704 b, a pulse width modulation (PWM) generator 707 and gate drivers 708 a, 708 b. The tunable capacitor circuit 700 is similar to that described in reference to FIG. 3, and includes an additional set of comparators 710 a, 710 b.

The controller 702 can be, for example, a microcontroller, a computer processor, an FPGA, or an ASIC. The controller 702 can include or be coupled to a computer readable storage device such as, for example, random access memory, flash memory, or other appropriate memory device. In some examples, the counters 704 a, 704 b can be internal counters in the controller 702. The controller 702 receives one or more input tuning signals and controls the PWM generator 707 to adjust the effective capacitance of the capacitors 302 a, 302 b based on the input tuning signal(s).

The PWM generator 707 generates PWM signals used to control the switches 304 a, 304 b. The ON timing, or ZVS timing, of the switches 304 a, 304 b is controlled by the phase of the PWM signals and the OFF timing, or T_(ON), is controlled by the duty cycle of the PWM signals. For example, the duty cycle is increased to increase the T_(ON) duration and reduced to decrease the T_(ON) duration. The period of the PWM signals is configured to match that of the signal applied to the capacitors 302 a, 302 b (Va, Vb). Thus, for example, for a 6.78 MHz signal applied to the capacitors 302 a, 302 b, the period of the PWM signals would be approximately 147.5 ns. The gate drivers 708 a, 708 b amplify the PWM signals as applicable to operate the switches 304 a, 304 b.

As described in reference to control circuitry 306 of FIG. 3, the control circuitry 706 controls the ZVS of the switches 304 a, 304 b and the effective capacitance of the capacitors 302 a, 302 b by controlling the shorting duration T_(ON). In addition, the control circuitry 706 adjusts the ZVS timing for turning the switches 304 a, 304 b ON to account for switching control delays. For example, electronic circuitry has some inherent signal processing and propagation delays, which become more readily apparent when circuits are operated at higher frequencies because delay times represent greater portions of operating signal periods. The control circuitry 706 can monitor such delays and adjust the ZVS timing for the switches 304 a, 304 b accordingly.

The comparators 710 a, 710 b are used to monitor the control signals applied to the switches 304 a, 304 b. More specifically, when transistors (e.g., MOSFETs) are used for the switches 304 a, 304 b, the comparators 710 a, 710 b can be configured to monitor for a voltage slightly below the threshold voltage, for example, the threshold voltage less a voltage offset (δ) (V_(th)—δ). The magnitude of the voltage offset (δ) is less than the magnitude of the threshold voltage (V_(th)) of the associated transistor.

For example, as shown in FIG. 7, the non-inverting (“+”) input terminal of each comparator 710 a, 710 b is electrically connected to the control terminal (e.g., gate) of its respective switch 304 a, 304 b. The inverting (“−”) input terminal of each comparator 710 a, 710 b is electrically connected to a reference voltage V₁ or V₂ for the respective switch 304 a, 304 b. The reference voltages, V₁ and V₂, can be set at the threshold voltage (V_(th)) of the associated switch 304 a, 304 b or the threshold voltage less a voltage offset (V_(th)−δ). In this configuration, each comparator 710 a, 710 b will output a high signal value when the voltage of the gate drive signal for its respective switch 304 a, 304 b exceeds the applicable reference voltage V₁ or V₂, thereby, indicating that the respective switch 304 a, 304 b is ON.

As illustrated in FIG. 7, the control circuitry 706 is symmetric, so, for simplicity, the control circuitry will be described in the context of controlling only one of the switch/capacitor pairs (switch 304/capacitor 302 a). The counter 704 a and controller 702 control the ZVS timing for the switch 304 a. The counter 704 a receives timing input signals from both comparator 308 a and comparator 710 a. As described above, the output signal of comparator 308 a indicates when the voltage across the capacitor 302 a (Va) crosses zero, and the output signal of comparator 710 a indicates when the switch 304 a turns ON. The counter 704 a measures the delay in turning the switch 304 a ON (“switching delay”) by measuring the timing difference between the output signals of comparator 308 a and comparator 704 a. For example, the counter 704 a can initiate a timer when an appropriate edge (rising or falling) of the output signal from comparator 308 a is received, and stop the timer when the output signal of comparator 710 a indicates that sufficient drive voltage is being applied to switch 304 a to turn switch 304 a ON.

The measured switching delay is provided to the controller 702. The controller 702 provides control signals to the PWM generator 707 to shift the phase of the PWM signal sent to gate driver 708 a in order to decrease the switching delay for switch 304 a. For example, the phase of the PWM signal sent to gate driver 708 a can be advanced by an amount equivalent to the measured switching delay. In some examples, the controller 702 can monitor the switching delay each time the switch 304 a is turned ON, and make adjustments to the PWM signal as appropriate. In some examples, the controller 702 can adjust the PWM signal until the switching delay is minimized. That is, the controller 702 can adjust the PWM signal until the switching delay is zero or approximately zero within the limitations of the circuit components (e.g., within the precision of the counters 704 a, 704 b).

FIG. 8 depicts the dynamically tunable capacitor circuit 800 with an example of a third implementation of the control circuitry 806. The control circuitry 806 includes a controller 802, phase detection circuits 804 a, 804 b, integrator circuits 805 a, 805 b, comparators 807 a, 807 b, flip-flops 809 a, 809 b, and gate drivers 808 a, 808 b. The tunable capacitor circuit 800 is similar to that described in reference to FIG. 3, and includes voltage divider circuits 812 a, 812 b and an additional set of comparators 810 a, 810 b.

The controller 802 can be, for example, a microcontroller, a computer processor, an FPGA, or an ASIC. The controller 802 can include or be coupled to a computer readable storage device such as, for example, random access memory, flash memory, or other appropriate memory device. In some examples, the controller 802 can be a PWM generator.

As described in reference to control circuitry 306 of FIG. 3, the control circuitry 806 controls the ZVS of the switches 304 a, 304 b and the effective capacitance of the capacitors 302 a, 302 b by controlling the shorting duration T_(ON). In addition, the control circuitry 806 adjusts the ZVS timing for turning the switches 304 a, 304 b ON to account for switching control delays. For example, electronic circuitry typically has at least some inherent signal processing and propagation delays, which become more readily apparent when circuits are operated at higher frequencies because delay times represent greater portions of operating signal periods. The control circuitry 806 can monitor such delays and adjust the ZVS timing for the switches 304 a, 304 b accordingly.

The comparators 810 a, 810 b monitor the control signals applied to the switches 304 a, 304 b. More specifically, when transistors (e.g., MOSFETs) are used for the switches 304 a, 304 b, the comparators 810 a, 810 b detect when the gate drive signals meet the threshold voltage (V_(th)) of the associated transistor. In some examples, the comparators 810 a, 810 b monitor for a voltage slightly below the threshold voltage, for example, the threshold voltage less a voltage offset (δ_(th)) Vth−δ_(th). The voltage offset (δ_(th)) can be positive if soft switching is desired, or negative if hard switching is desired. The magnitude of the voltage offset (δ_(th)) is less than the magnitude of the threshold voltage (V_(th)) of the associated transistor.

For example, as shown in FIG. 8, the non-inverting (“+”) input terminal of each comparator 810 a, 810 b is electrically connected to the control terminal (e.g., gate) of its respective switch 304 a, 304 b. The inverting (“−”) input terminal of each comparator 810 a, 810 b is electrically connected to a reference voltage V₁ or V₂ for the respective switch 304 a, 304 b. The reference voltages, V₁ and V₂, can be set at the threshold voltage (V_(th)) of the associated switch 304 a, 304 b or the threshold voltage less a voltage offset (Vth−δ_(th)). In this configuration, each comparator 810 a, 810 b will output a high signal value when the voltage of the gate drive signal (Vg) for its respective switch 304 a, 304 b exceeds the applicable reference voltage V₁ or V₂, thereby, indicating that the respective switch 304 a, 304 b is ON. In some implementations, the reference voltages V₁ or V₂ are equal. Further, in some implementations, the inverting input terminals of both comparator 810 a and 810 b can be electrically connected to a common reference voltage (e.g., V₁ or V₂). Alternatively, reference voltages V₁ and V₂ can be different and can be provided as independent reference voltages.

The voltage divider circuits 812 a, 812 b are optionally used in tunable capacitor circuits 800 that operate at high voltages that would otherwise damage comparators 308 a, 308 b, 807 a, and 807 b, and possible other portions of the control circuitry 806. The voltage divider circuits 821 a, 812 b step the operating voltages of the tunable capacitors circuits 800 (e.g., Va and Vb) down to voltage levels that the control circuitry 806 can manage without incurring damage. Each voltage divider circuit 812 a, 812 b includes a network of resistive elements 816 and impedance elements 814 (e.g., capacitors and/or inductors) of appropriate values to step down the voltage from the tunable capacitor circuit for control circuitry 806. Although the voltage divider circuits 812 a, 812 b are illustrated expressly in FIG. 8, they can be included in any of the preceding implementations as well.

As illustrated in FIG. 8, the control circuitry 806 is symmetric, so, for simplicity, the control circuitry will be described in the context of controlling only one of the switch/capacitor pairs (switch 304 a/capacitor 302 a). However, it should be understood that the following discussion applies equally to the control of other switch capacitor pairs (e.g., switch 304 b/capacitor 302 b). The phase detection circuit 804 a is coupled with the output terminals of comparator 308 a and 810 a and receives the output signals of comparator 308 a and 810 a as the phase detection circuit 804 a input signals. The output of the phase detection circuit 804 a is coupled with the input to the integrator circuit 805 a. Together, the phase detection circuit 804 a and the integrator circuit 805 a generate a reference voltage (V_(int)) input to comparator 807 a.

The comparator 807 a monitors the voltage across the switch 304 a and capacitor 302 a (Va) with respect to the reference voltage (V_(int)) generated by the phase detection circuit 804 a and integrator circuit 805 a. The non-inverting (“+”) input terminal of comparator 807 a is coupled with the integrator circuit 805 a. The inverting (“−”) input terminal of comparator 807 a is electrically connected to the non-grounded terminals of the switch 304 a and the capacitor 302 a. Consequently, the comparator 807 a inverts its output signal when the signal at the inverting input terminal (e.g., voltage Va or Va divided by the optional voltage divider circuit 812 a) falls below the reference voltage (V_(int)).

The flip-flop 809 a receives the output signal of comparator 807 a at an edge triggered clock terminal. The rising edge of the comparator 807 a output signal causes the flip-flop 809 a to output the voltage signal (VDD) applied to the input terminal (D) of the flip-flop 809 a, thereby, turning on the switch 304 a. The output terminal (Q) of the flip-flop 809 a is electrically connected to the control terminal of the switch 304 a (e.g., transistor gate) through the optional gate driver 808 a. The controller 802 is coupled with the reset terminal (CLR) of the flip-flop 809 a and sends a reset signal to the flip-flop 809 a to open (or turn OFF) the switch 304 a after the capacitor shorting duration T_(ON).

In operation, the phase detection circuit 804 a, integrator circuit 805 a, and comparator 807 a control when the switch 304 a closes (e.g., a transistor turns ON). In other words, the phase detection circuit 804 a, integrator circuit 805 a, and comparator 807 a control the ZVS timing for the switch 304 a. The phase detection circuit 804 a and integrator circuit 805 a adaptively generate a reference voltage (V_(int)) for the comparator 807 a that accounts for the control circuitry's 806 switching delay. The reference voltage (V_(int)) is established so as to cause the comparator 807 a to begin the switching process (the process of turning switch 304 a ON) an appropriate amount of time before the voltage across the switch 304 a and capacitor 302 a (Va) crosses zero such that the switch 304 a will begin conducting (turn ON) at the zero crossing instead of, for example, several nanoseconds afterwards. The comparator 807 a monitors the voltage across the switch 304 a and capacitor 302 a (Va) and inverts its output signal when Va (or Va divided by the optional voltage divider circuit 812 a) falls below the output voltage of the of the integrator circuit 805 a (V_(int)), thereby, causing the flip-flop 809 a to turn on the switch 304 a.

More specifically, as noted above, comparator 308 a monitors the voltage across the capacitor 302 a. When the voltage (Va) across capacitor 302 a (and switch 304 a) is at (or near) zero, the output signal of comparator 308 a switches states. Thus, the output signal of comparator 308 a is timed to the zero crossings of the voltage across the capacitor 302 a and switch 304 a. Also, as noted above, comparator 810 a monitors the control signal applied to switch 304 a. When the voltage at the control terminal of switch (Vg) is at or exceeds the threshold voltage (V₁), the output signal of comparator 810 a switches states. The threshold voltage (V₁) is set at or just below the voltage required to turn switch 304 a ON, thus, the output signal of comparator 810 a is timed to indicate when the switch 304 a turns ON.

The phase detection circuit 804 a determines a phase difference between output signals from comparator 308 a and comparator 810 a, which represents the time delay between when the comparator 308 a detects the voltage Va crossing zero and when the switch 304 a actually turns ON to short out the capacitor 302 a. The phase detection circuity 804 a outputs a voltage signal proportional to this phase difference each time the switch 304 a is turned ON. The integrator circuit 805 a sums the phase detection circuity 804 a output signals, the result of which is provided as a reference voltage (V_(int)) for the non-inverting input terminal of comparator 807 a. Because the reference voltage (V_(int)) applied to comparator 807 a is slightly above zero, the comparator 807 a will begin the switching process for switch 304 a before the voltage Va actually crosses zero. This provides sufficient time for the voltage at the control terminal of switch 304 a to build up to a value sufficient to turn the switch 304 a ON when the voltage Va does cross zero.

FIGS. 9A-9D depict graphs of exemplary control signals in the control circuitry 806. FIG. 9A depicts a graph 900 of the voltage across the switch 304 a and capacitor 302 a (Va) and the voltage applied to the control terminal of switch 304 a (Vg) at 1 μs after applying a voltage signal to the tunable capacitor circuit 800. The voltage signal Va is a 6.78 MHz sinusoidal signal. The graph 900 shows the signals Va and Vg before the control circuitry 806 has had time to adjust for the switching delay 902. At point 904 Va crosses zero volts and the control circuitry 806 begins applying the gate voltage (Vg) to the control terminal of the switch 304 a. However, the gate voltage (Vg) does not reach the threshold voltage (e.g., 1.5 V) of the switch 304 a until point 906. Therefore, due to the switching delay 902, the voltage across the switch 304 a and capacitor 302 a (Va) is allowed to drop significantly below zero volts before the switch 304 a turns on at point 906. The total switching delay 902 is approximately 3.63 ns and represents approximately 2.5% of the period of the voltage signal Va.

However, over a short period of time the phase detection circuit 804 a and integrator circuit 805 a adjust the reference voltage (V_(int)) of comparator 807 a to account for the switching delay 902 to shift point 904 and begin applying the gate voltage (Vg) to the switch 304 a earlier in time. For example, FIG. 9B depicts a graph 925 showing an example of the integrator circuit 805 a output signal (V_(int)) (also the reference voltage for comparator 807 a) varying over time. At 1 μs after applying a voltage signal to the tunable capacitor circuit 800 (point 926), the voltage signal V_(int) is relatively small. Thus, comparator 807 a is not triggering the flip-flop 809 a to turn on the switch until the voltage across the switch 304 a and capacitor 302 a (Va) is already too close to zero to account for the switching delay. The voltage signal V_(int) begins to plateau at approximately 18 μs and ZVS is fairly achieved at approximately 34 μs after applying a voltage signal (point 928). Note that continuous reduction in the slope of the voltage signal V_(int) illustrates the decreasing phase difference between the output signals of comparators 308 a and 810 a as the switch timing approaches ZVS.

FIG. 9C depicts a graph 950 of the voltage across the switch 304 a and capacitor 302 a (Va) and the voltage applied to the control terminal of switch 304 a (Vg) at approximately 34 μs after applying a voltage signal to the tunable capacitor circuit 800. Here, the control circuitry 806 begins applying the gate voltage (Vg) to the control terminal at point 952 of the switch 304 a when the voltage Va is approximately 5.5 V. Thus, the gate voltage Vg reaches the threshold voltage (e.g., 1.5 V) of the switch 304 a at point 906 within approximately 20 ps of when the voltage signal Va crosses zero (point 904). The voltage signal Va still drops slightly below zero, however, more due to ringing than switching delay.

Referring again to FIG. 8, the controller 802 controls the capacitor shorting duration (T_(ON)) (e.g., the time that the switch 304 a is maintained ON). For example, the controller 802 can include a timer that is triggered to start when the switch 304 is turned ON. At the expiration of the timer the controller 802 sends a reset signal to the flip-flop 809 a causing the flip-flop 809 a to turn the switch 304 a OFF by, for example, ceasing to apply the required voltage to the control terminal of the switch 304 a. The controller 802 can vary the value of T_(ON) based on an input signal received by the controller 802. For example, the controller 802 may receive the input signal from an impedance matching network control circuit.

FIG. 9D depicts a graph 975 of the current (I_(AC)) flowing into capacitor 302 a and the switch 304 a, the voltage across the switch 304 a and capacitor 302 a (Va), and the voltage applied to the control terminal of switch 304 a (Vg). Graph 975 illustrates the full operation of control circuitry 806. At point 952 the control circuitry 806 begins to apply a gate voltage signal (Vg) to the control terminal of the switch 304 a, slightly before the voltage signal Va crosses zero at point 904. At point 906 the value of the gate voltage signal Vg is sufficient to turn the switch 304 a ON. The controller 802 resets the flip-flop 809 a at point 976 after the shorting duration (T_(ON)) 980 expires. At point 978 the gate voltage signal decays sufficiently to turn the switch 304 a OFF and the capacitor 302 a begins to charge. The controller 802 turns switch 304 a OFF during the positive half 982 of the current I_(AC) so that the voltage signal Va is rising.

Referring back to FIG. 8, in some implementations the controller 802 can be a PWM generator. In such implementations, the PWM generator can output a PWM signal to the reset terminal of the flip-flop 809 a. The shorting duration (T_(ON)) can be controlled by the PWM signal. For example, the frequency of the PWM signal can be matched to that of the voltage signal Va applied to the capacitor 302 a and the switch 304 a. The shorting duration (T_(ON)) can be controlled by the phase of the PWM signal pulse relative to the phase of the voltage signal Va. For example, the amount of phase delay between the rising edge of the PWM pulse and the zero crossing on the negative slope of the voltage signal Va can be set to achieve a desired shorting duration (T_(ON)).

In some implementations, the voltage offset (δ_(th)) of reference voltages V₁ and V₂ can be adjustable. For example, the voltage offset (δ_(th)) can be the output of a digital to analog converter (DAC). The input to the DAC can be a digital output signal from the controller 802. For example, an adjustable voltage offset (δ_(th)) may permit fine tuning of the ZVS points. For instance, decreasing the magnitude of the voltage offset (δ_(th)) biases the control circuitry 806 towards switching closer to the actual zero crossing point of the applied voltage signal. Furthermore, decreasing the voltage offset (δ_(th)) to zero or a negative value can place the control circuitry 806 into a hard switching mode.

In some implementations, the comparators 308 a, 308 b are referenced to ground. That is, the non-inverting inputs of comparators 308 a, 308 b are connected to ground, for example, as in FIG. 3. In some implementations, the comparators 308 a, 308 b can be referenced to a slightly positive voltage (V_(GND)+δ). That is, the non-inverting inputs of comparators 308 a, 308 b can be connected to a slightly positive voltage (V_(GND)+δ). In some examples, the δ voltage can be set to reduce the initial switching delay (e.g., that shown in FIG. 9A) and reduce the time required for the control circuitry 806 to generate an optimal reference voltage (V_(int)) for comparator 805 a. In some examples, the δ voltage can be set to bias the control circuitry 806 more towards hard switching versus soft switching. Furthermore, the δ voltage can be either a preset value or adjustable.

The examples and implementations discussed above are described in reference to performing ZVS on the positive half of a voltage waveform. It should be understood that the implementations discussed can also perform ZVS on the negative half of a voltage waveform. To do so, the polarity of reference signals can be reversed and the connections to the input terminals of appropriate comparators can be switched. In addition, the connections to the input terminals of the comparators shown in the depicted circuits can be switched for use with falling edge triggered devices (e.g., flip-flops) instead of rising edge triggered devices.

In some examples, the control circuitry of each of the above described tunable capacitor circuits can be implemented as ZVS circuitry in other applications. For example, the control circuitry of any of the above described implementations can be used as ZVS control circuitry for various amplifiers or power supplies (e.g., class D or class E switching amplifiers). For example, the ZVS devices and methods described herein can be used to control the switch timing of amplifiers or power supplies to minimize power losses in the amplifier or power supply. Zero voltage amplifier switching may also reduce hard switching effects and electromagnetic interference effects in amplifiers.

For illustrative purposes, the foregoing description focuses on the use of devices, components, and methods in desktop wireless power transfer applications, e.g., power transfer to electronic devices such as laptops, smartphones, and other mobile electronic devices that are commonly placed on desktops, tabletops, and other user work surfaces.

More generally, however, it should be understood that devices that can receive power using the devices, components, and methods disclosed herein can include a wide range of electrical devices, and are not limited to those devices described for illustrative purposes herein. In general, any portable electronic device, such as a cell phone, keyboard, mouse, radio, camera, mobile handset, headset, watch, headphones, dongles, multifunction cards, food and drink accessories, and the like, and any workspace electronic devices such as printers, clocks, lamps, headphones, external drives, projectors, digital photo frames, additional displays, and the like, can receive power wirelessly using the devices, components, and methods disclosed herein. Furthermore, any electrical device, such as electric or hybrid vehicles, motorized wheel chairs, scooters, power tools, and the like, can receive power wirelessly using the devices, components, and methods disclosed herein. In addition the devices, components, and methods disclosed herein may be used for applications outside of wireless power transfer, for example, power factor correction devices, handheld signal analyzers, and the like.

In this disclosure, certain circuit or system components such as capacitors, inductors, resistors, diodes, and switches, are referred to as circuit “components” or “elements.” The disclosure also refers to series and parallel combinations of these components or elements as elements, networks, topologies, circuits, and the like. Further, combinations of capacitors, diodes, transistors, and/or switches are described. More generally, however, where a single component or a specific network of components is described herein, it should be understood that alternative embodiments may include networks for elements, alternative networks, and/or the like.

As used herein, the term “coupled” when referring to circuit or system components is used to describe an appropriate, wired or wireless, direct or indirect, connection between one or more components through which information or signals can be passed from one component to another.

As used herein, the term “direct connection” or “directly connected,” refers to a direct connection between two elements where the elements are connected with no intervening active elements between them. The term “electrically connected” or “electrical connection,” refers to an electrical connection between two elements where the elements are connected such that the elements have a common potential. In addition, a connection between a first component and a terminal of a second component means that there is a path between the first component and the terminal that does not pass through the second component.

The embodiments described herein merely serve to illustrate, but not limit, the features of the disclosure. Other embodiments are also within the scope of the disclosure. 

What is claimed is:
 1. A variable capacitance device comprising: a first capacitor comprising a first-capacitor first terminal and a first-capacitor second terminal, the first-capacitor first terminal electrically connected to a ground; a first switch comprising a first-switch first terminal, a first-switch second terminal, and a first-switch control terminal, the first-switch first terminal electrically connected to the first-capacitor first terminal, and the first-switch second terminal electrically connected to the first-capacitor second terminal; a first comparator comprising a first-comparator first input terminal electrically connected to the first-capacitor second terminal; a second capacitor comprising a second-capacitor first terminal and a second-capacitor second terminal, the second-capacitor first terminal electrically connected to the ground; a second switch comprising a second-switch first terminal, a second-switch second terminal, and a second-switch a control terminal, the second-switch first terminal electrically connected to the second-capacitor first terminal, and the second-switch second terminal electrically connected to the second-capacitor second terminal; a second comparator comprising a second-comparator first input terminal electrically connected to the second-capacitor second terminal; and control circuitry coupled with the first-switch control terminal, with the second-switch control terminal, with a first-comparator output terminal of the first comparator, and with a second-comparator output terminal of the second comparator, wherein the control circuitry is configured to adjust respective capacitances of the first and second capacitors by: detecting a zero voltage condition across the first switch based on an output signal of the first comparator, and, in response, cause a first control signal to be applied to the first-switch control terminal for a duration of time, wherein the first control signal causes the first switch to close; and detecting a zero voltage condition across the second switch based on an output signal of the second comparator, and, in response, cause a second control signal to be applied to the second-switch control terminal for the duration of time, wherein the second control signal causes the second switch to close.
 2. The variable capacitance device of claim 1, wherein a capacitance of the device depends on the duration of time for which the first and second control signals are applied to the respective first-switch control terminal and second-switch control terminal.
 3. The variable capacitance device of claim 1, wherein the first switch is a first transistor and the second switch is a second transistor.
 4. The variable capacitance device of claim 1, wherein the control circuitry is configured to receive an input signal and, in response to receiving the input signal, change the duration of time for which the first and second control signals are applied to the respective first-switch control terminal and second-switch control terminal.
 5. The variable capacitance device of claim 1, further comprising: a third comparator comprising a third-comparator first input terminal electrically connected to a first reference voltage and a third-comparator second input terminal electrically connected to the first-switch control terminal; and a fourth comparator comprising a fourth-comparator first input terminal electrically connected to a second reference voltage and a fourth-comparator second input terminal electrically connected to the second-switch control terminal; wherein the control circuitry is coupled with a third-comparator output terminal of the third comparator and a fourth-comparator output terminal of the fourth comparator, and the control circuitry is configured to: detect a first ON condition at the first-switch control terminal based on an output signal of the third comparator; determine a first time difference, the first time difference being a difference in time from detecting the zero voltage condition across the first switch and detecting the first ON condition at the first-switch control terminal; adjust a first timing of when the first control signal is applied to the first-switch control terminal so as to reduce the first time difference; detect a second ON condition at the second-switch control terminal based on an output signal of the fourth comparator; determine a second time difference, the second time difference being a difference in time from detecting the zero voltage condition across the second switch and detecting the second ON condition at the second-switch control terminal; and adjust a second timing of when the second control signal is applied to the second-switch control terminal so as to reduce the second time difference.
 6. The variable capacitance device of claim 5, wherein the control circuitry comprises: a pulse width modulation (PWM) generator comprising a first output terminal electrically connected to the first-switch control terminal and a second output terminal electrically connected to the second-switch control terminal, wherein the first control signal is a first pulse width modulated signal and the second control signal is a second pulse width modulated signal, and wherein the control circuitry is configured to control characteristics of the first and second pulse width modulated signals.
 7. The variable capacitance device of claim 6, wherein adjusting the timing of when the first and second control signals are applied to the respective first-switch control terminal and the second-switch control terminal comprises adjusting phases of the first and second pulse width modulated signals.
 8. The variable capacitance device of claim 6, wherein the control circuitry is configured to receive an input signal and, in response to receiving the input signal, change the duration of time for which the first and second control signals are applied to the respective control terminals of the first switch and the second switch by adjusting respective duty cycles of the first and second pulse width modulated signals.
 9. The variable capacitance device of claim 1, further comprising: a third comparator comprising a third-comparator first input terminal electrically connected to a first reference voltage and a third-comparator second input terminal electrically connected to the first-switch control terminal; and a fourth comparator comprising a fourth-comparator first input terminal electrically connected to a second reference voltage and a fourth-comparator second input terminal electrically connected to the second-switch control terminal; and wherein the control circuitry comprises: a controller; a first counter coupled with the first-comparator output terminal, the third-comparator output terminal, and the controller, the first counter configured to: start a first timer in response to receiving a zero voltage signal from the first comparator, stop the first timer in response to receiving a first ON condition signal from the third comparator, and send a signal indicating an elapsed time of the first timer to the controller; and a second counter coupled with the second-comparator output terminal, the fourth-comparator output terminal, and the controller, the second counter configured to: start a second timer in response to receiving a zero voltage signal from the second comparator, stop the second timer in response to receiving a second ON condition signal from the fourth comparator, and send a signal indicating an elapsed time of the second timer to the controller; wherein the controller is configured to: adjust, based on the first-time-difference signal, a first timing of when the first control signal is applied to the first-switch control terminal so as to reduce the first time difference; and adjust, based on the second-time-difference signal, a second timing of when the second control signal is applied to the second-switch control terminal so as to reduce the second time difference.
 10. The variable capacitance device of claim 9, wherein the control circuitry comprises: a pulse width modulation (PWM) generator coupled with the controller, the PWM generator comprising a first output terminal electrically connected to the first-switch control terminal and a second output terminal electrically connected to the second-switch control terminal, wherein the first control signal is a first pulse width modulated signal and the second control signal is a second pulse width modulated signal, and wherein the controller is configured to control characteristics of the first and second pulse width modulated signals.
 11. The variable capacitance device of claim 9, wherein the controller is one of: a microcontroller, a computer processor, a field programmable logic array (FPGA), or an application specific integrated circuit (ASIC).
 12. The variable capacitance device of claim 1, further comprising: a third comparator comprising a third-comparator first input terminal electrically connected to a first reference voltage and a third-comparator second input terminal electrically connected to the first-switch control terminal; and a fourth comparator comprising a fourth-comparator first input terminal electrically connected to a second reference voltage and a fourth-comparator second input terminal electrically connected to the second-switch control terminal; wherein detecting the zero voltage condition across the first switch based on an output signal of the first comparator, and, in response, causing the first control signal to be applied to the first-switch control terminal comprises: determining a first phase difference between a first-comparator output signal and a third-comparator output signal, generating a third reference voltage based the first phase difference, and causing the first control signal to be applied to the first-switch control terminal upon detecting that a voltage signal at the first-switch second terminal has crossed a voltage value equal to the third reference voltage, and wherein detecting the zero voltage condition across the second switch based on an output signal of the second comparator, and, in response, cause the second control signal to be applied to the second-switch control terminal comprises: determining a second phase difference between a second-comparator output signal and a fourth-comparator output signal, generating a fourth reference voltage based the second phase difference, and causing the second control signal to be applied to the second-switch control terminal upon detecting that a voltage signal at the second-switch second terminal has crossed a voltage value equal to the fourth reference voltage.
 13. The variable capacitance device of claim 12, wherein the control circuitry comprises: a first phase detection circuit coupled with the first-comparator output terminal and a third-comparator output terminal of the third comparator; a first integrator circuit coupled with the first phase detection circuit; a fifth comparator comprising a fifth-comparator output terminal, a fifth-comparator first input terminal electrically connected to the first-capacitor second terminal, and a fifth-comparator second input terminal coupled with the first integrator circuit; a first flip-flop comprising a first-flip-flop reset terminal, a first-flip-flop clock terminal electrically connected to the fifth-comparator output terminal, and a first-flip-flop output terminal electrically connected to the first-switch control terminal; a second phase detection circuit coupled with the second-comparator output terminal and a fourth-comparator output terminal of the fourth comparator; a second integrator circuit coupled with the second phase detection circuit; a sixth comparator comprising a sixth-comparator output terminal, a sixth-comparator first input terminal electrically connected to the second-capacitor second terminal, and a sixth-comparator second input terminal coupled with the second integrator circuit; a second flip-flop comprising a second-flip-flop reset terminal, a second-flip-flop clock terminal electrically connected to the sixth-comparator output terminal, and a second-flip-flop output terminal electrically connected to the second-switch control terminal; and a controller coupled with the first flip-flop and the second flip-flop and configured to provide a first reset signal to the first flip-flop after the duration of time and to provide a second reset signal to the second flip-flop after the duration of time.
 14. The variable capacitance device of claim 13, wherein the controller is a pulse width modulation (PWM) generator, the first reset signal is a first pulse width modulated signal, and the second reset signal is a second pulse width modulated signal.
 15. A wireless energy transfer system comprising: a split coil resonator comprising a first winding magnetically coupled with a second winding, wherein the first winding comprises a first-winding terminal and a third-winding terminal, and wherein the second winding comprises a second-winding terminal and fourth-winding terminal; a fixed impedance matching network coupled with the third-winding terminal of the first winding and the fourth-winding terminal of the second winding; and a variable capacitance device comprising: a first capacitor comprising a first-capacitor first terminal and a first-capacitor second terminal, the first-capacitor first terminal electrically connected to a ground, and the first-capacitor second terminal electrically connected to a first-winding terminal of the first winding of the split coil resonator; a first switch comprising a first-switch first terminal, a first-switch second terminal, and a first-switch control terminal, the first-switch first terminal electrically connected to the first-capacitor first terminal, and the first-switch second terminal electrically connected to the first-capacitor second terminal; a second capacitor comprising a second-capacitor first terminal and a second-capacitor second terminal, the second-capacitor first terminal electrically connected to the ground, and the second-capacitor second terminal electrically connected to a second-winding terminal of the second winding of the split coil resonator; a second switch comprising a second-switch first terminal, a second-switch second terminal, and a second-switch a control terminal, the second-switch first terminal electrically connected to the second-capacitor first terminal, and the second-switch second terminal electrically connected to the second-capacitor second terminal; and control circuitry coupled with the first-switch control terminal and with the second-switch control terminal, wherein the control circuitry is configured to adjust respective capacitances of the first and second capacitors by: in response to detecting a zero voltage condition across the first switch, causing a first control signal to be applied to the first-switch control terminal for a duration of time, wherein the first control signal causes the first switch to close; and in response to detecting a zero voltage condition across the second switch, causing a second control signal to be applied to the second-switch control terminal for the duration of time, wherein the second control signal causes the second switch to close.
 16. The wireless energy transfer system of claim 15, further comprising: a third capacitor comprising a third-capacitor first terminal and a third-capacitor second terminal, the third-capacitor first terminal electrically connected to the first-winding terminal, and the third-capacitor second terminal electrically connected to the first-capacitor second terminal; and a fourth capacitor comprising a fourth-capacitor first terminal and a fourth-capacitor second terminal, the fourth-capacitor first terminal electrically connected to the second-winding terminal, and the fourth-capacitor second terminal electrically connected to the second-capacitor second terminal.
 17. The wireless energy transfer system of claim 15, further comprising a third capacitor comprising a third-capacitor first terminal and a third-capacitor second terminal, the third-capacitor first terminal electrically connected to the first-winding terminal, and the third-capacitor second terminal electrically connected to the second-winding terminal.
 18. The wireless energy transfer system of claim 15, wherein a capacitance of the variable capacitance device depends on the duration of time for which the first and second control signals are applied to the respective first-switch control terminal and second-switch control terminal. 